I’ve seen more than once lefties playing right handed guitars/basses upside down. I’ve always wondered how practical that was and if it impacted the tone or not. I suppose if you rotate the nut, string, and pickups that it’s pretty much a left-handed instrument then? I mean, clearly it works, because Hendrix didn’t have any issues. 
That could be a way to buy a bass you want, even if it is just made for right-hand playing. Don’t take my word for it though!
Good old Jimi . . . 
Popular Mechanics magazine had an article in 2015, about the then-new release by Fender of a “Jimi Hendrix Stratocaster” which was set up as his had been. The article describes how the tension, etc. was affected due to pickup and string length.
To add my 2 cents several times over on this topic:
Regarding handedness, and being a left hander myself, I had the interest to read several books over the years on the topic (not the type of book telling you which famous people are left handed, but more academic books). This does not make me any kind of expert, but I did retain a few bits of information to share.
1. Ambidexterity: this seems to be a term that is used vaguely, but actually has a specific meaning: the ability to use both hands equally well.
Not “doing some things better with one hand, but can do the same thing to some degree with the other hand,” or doing certain things with one hand only, and other things only with the other; but equally well with both hands. It is therefore rare to be truly ambidextrous.
2. “Mixed handedness”, or degrees of being left or right handed: Most right handed people do everything with their right hand, both in fine motor and gross motor skills. Some left handers do everything with their left hand, but most fall into a range of some degree of using different hands for different tasks. You can find various questionnaires online to determine how strongly you are left or right handed. We usually define people as being left handed because they use their left hand to write.
As far as a newbie learning the bass, the left handed person who wants to learn is the only one who can determine if playing left handed or right handed is correct in his or her situation. Barring physical considerations which might have bearing on the decision (injuries or illnesses affecting one hand or the other), it would be best to pick up a bass (or guitar) and see which way feels the most natural to you.
If you think you will be unduly restricted by the lack of models of left handed bass guitars available in the future (assuming you plan on continuing to play bass), then obviously that is a consideration, too, if you can train yourself to play right handed from the start. And for someone who started many years ago, when left handed models of guitars and basses were more rare, you had to either play right handed, switch the strings, or play the instrument upside down.
Personally, I determined long ago that I use my left hand for fine motor skills (such as writing, brushing teeth, using scissors), and my right for gross motor (throwing, using a bat, tennis racquet, etc.). But I do rake leaves and shovel snow left handed. I have a left handed sister who is almost as left handed as most right handed people are completely right handed. She doesn’t play bass or guitar, though. 
I think in my case, for playing a stringed instrument: the moving of the arm up and down the frets is gross motor, aside from the fingers fretting, which does require some amount of strength as well as dexterity. Playing a left handed model does feel natural to me.
About the idea that left handers should get a right handed guitar/bass, because the “dominant” left hand would do the fretting; I think this is a deceptive argument. Why then don’t right hand dominant people all play left hand oriented guitars/basses?
It all boils down to the individual’s particular case.
Exactly! As a 100%, unequivocal, indubitable and absolute righty, I can tell you this: not in a thousand years would I be able to learn how to play bass left handed.
Casting aside matters of instrument availability, etc., I decided to stay lefty on the bass because I had a solid forty-plus years of lefty air guitar under my belt when I decided to pick up the bass again last year. Playing righty would have been as natural as trying to teach myself to write righthanded after a lifetime of writing lefty. (Also, I bought a bass before seeing what Josh said about being a lefty playing righty.)
Medically mixed handedness and ambidextrous are interchangeable terms.
Interesting. I’m not a doctor and do not play one on the internet. 
The definitions I gave were: Ambidexterity from Dictionary.com, and Mixed Handedness from what I remembered reading.
Apparently Mixed Handedness is also called Cross-Dominance. The definition for ambidexterity is a literal one, but probably too literal for the way most use it.
Here’s a page which has comments by left handed people, about playing guitar, bass, and other instruments. Most seem to have chosen to play right handed.
Here’s the thing, ambidexterity isn’t dependant on how you use your hands. People’s brains have hemispheres, right and left. People whose left hemisphere is dominant are right handed; vice versa for lefties.
If neither is dominant, then it’s called ambidextrous, which translated means both favorable
There is ambisinistral, where you use both hands but neither well. I think that’s what’s tripping up definitions.
As an ambidextrous person I find the lay definitions miss the mark, it’s more nuanced. But people like clean cut definitions. Human nature.
What’s a vegetable? Biologically the term isn’t meaningful. But people will tell you with certainty this is a fruit and that is a vegetable
I understand your point. But I also think that the concept of hemisphere dominance is a tricky question.
For the term ambisinistral, I came across it earlier today, in the context that some left handed people take issue with it, due to the use of “sinister” for the left hand, and the negative associations that go with it. As you say, ambidextrous means both favorable, showing the historical thinking of dexter (right) = good, and sinister (left) = bad. I don’t know if there are any non-judgmental terms to describe those situations.
As an ambidextrous person, do you play bass or guitar with either hand? Or do you prefer one for stringed instruments?
This is where I think the definitions are off, because I do some things right handed. But that’s mostly due to environmental conditioning. I write right handed because the nuns would rap my knuckles if I tried it left handed. I throw baseballs right handed because my glove was on my left hand. Other things I throw either handed.
I play right hand guitar because I’ve never seen a left. Maybe I’d play just fine. I switch hit in baseball.
But there are so many right handed basses I just go with the flow because it doesn’t matter to me which hand I use.
Which is why I find the ambidextrous/many handed definitions bollocks. Because it doesn’t matter to me so I go with the flow, and some things I do righty and some lefty. But it’s just habits
I get the sinister thing. In Latin it doesn’t have a bad connotation but in English it does. Will banish the term from my vocabulary. Thanks